CHAPTER 5 GRAVITY ANOMALY OVER EAST CHINA SEA AND TAIWAN
5.4 Outlier Distribution
The altimeter data we used are from the non-repeat missions ERS-1/GM and Geosat/GM, and the repeat missions Geosat/ERM, ERS-1/35-day, ERS-2/35-day and TOPEX/Poseidon 10-day repeats. Since no reliable estimate of SST is available here, it was set to zero. Neglecting SST here will introduce error at sub-mgal level (Hwang, 1997). For LSC computations, standard errors of the altimeter data are needed. For repeat missions, the standard errors of the altimeter data are derived from repeat observations, while for non-repeat missions, the standard errors are based on empirical values (Hwang et al., 2002). All altimeter data were screened against outliers using differenced heights. Figure 5.6 and 5.7 show the distribution of outliers over ECS and TS all altimeter missions. Outliers can occur anywhere in the oceans.
Table 5.2 and Table 5.3 show the summary of outlier rejection over ECS and TS respectively. The outliers in the open oceans come largely from the non-repeat missions (Geosat/GM and ERS-1/GM). Due to data editing in extracting SSHs from the geophysical data records (GDRs), most of the bad altimeter data in the immediate
vicinity of coasts have already been removed before outlier detection. In general, there is a higher concentration of outliers near the coasts and islands than other areas.
In particular, clusters of outliers were found at the southern Korean coast, the estuary of the Yangtze River and Peng-Hu Island over TS.
Figure 5.6: Distribution of altimeter data outliers in the East China Sea.
Figure 5.7: Distribution of altimeter data outliers in Taiwan Strait.
Table 5.2: Summary of outliers rejection in the East China Sea (119/131/25/35) data No. of passes No. of differenced ssh outliers Reject%
Geosat/gm 615 96392 873 0.9
Geosat/erm 37 15797 452 2.8
ERS2/35d 39 3509 80 2.2
ERS1/35d 37 3528 75 2.1
ERS1/gm 368 37173 334 0.9
Seasat 50 5631 67 1.2
T/P 12 1236 52 4.0
Table 5.3: Summary of outliers rejection around Taiwan (117/125/20/28)
data No. of passes No. of differenced ssh to be used outliers reject%
Geosat/gm 406 55579 555 1.0
5.5.1 The East China Sea
The first case study to assess the accuracies of gravity anomaly from the three altimeter-derived observations (mentioned in section 2.3 and 4.3) was carried out over ECS. We experimented with four cases of altimeter-gravity conversion. In these four cases, we used two methods of conversion: LSC and the inverse Vening Meinesz method (Hwang, 1998), and three altimeter-derived observations: DOV, differenced height and height slope. To identify the best case, we compared the altimeter-derived gravity anomalies with shipborne gravity anomalies. Figure5.1 shows the tracks of two selected ship cruises in the ECS (Tracks dmm07 and c1217) and two cruises in the TS (Tracks 1 and 2). The shipborne gravity data over ECS are from NGDC.
Before comparison, for each track we removed a bias and a trend in the shipborne gravity relative to the altimeter-derived gravity anomalies (Hwang and Parsons, 1995).
Table 5.4 shows the statistics of the differences between the altimeter-derived and shipborne gravity anomalies. The best result is from the case of using LSC with
differenced height, followed by the case of using LSC with height slope. The case of using LSC with DOV yields the least accurate gravity anomalies. Figure 5.8 shows the shipborne and altimeter-derived gravity anomalies along c1217 and dmm07. In general, the altimeter-derived gravity anomalies are smoother than the shipborne gravity anomalies. This is due to the filtering of the altimeter observations before the gravity derivations. At large spatial scales, the shipborne and altimeter-derived gravity anomalies agree very well, but at small spatial scales the differences become random and are not correlated with standard deviation of SSH, tidal difference or depth.
To see the possible sources causing the differences between altimeter-derived and shipborne gravity anomalies, we computed the normalized values of gravity anomaly differences (Case 1 gravity anomaly vs. shipborne gravity anomaly), depths, standard errors of ERS-1 SSH, tidal height differences (CSR4.0 vs. NAO 99) along Cruises c1217 and dmm07. As seen in Figure 5.9 and 5.10, the gravity anomaly differences fluctuate rapidly and do not possess a particular pattern with respect to the other three quantities. Over the shallow waters (depth less than 100 meters) of the ECS, both gravity anomaly differences and tidal height differences are relatively large.
In general, the standard error of ERS-1 SSH increases with decreasing depth.
Furthermore, the tidal height difference is larger over shallow waters than over the deep waters, and this agrees with the conclusion drawn in Section 5.2.
Table 5.4: Statistics of differences (in mgals) between altimeter-derived and shipborne gravity anomalies in East China Sea.
Case Mean RMS Min Max
LSC with differenced height -5.33 13.02 -49.24 43.96 LSC with height slope -5.45 13.19 -50.77 44.38
LSC with DOV -4.61 16.99 -85.59 74.65
Inverse Vening Meinesz with DOV -4.11 15.53 -52.23 80.53
Table 5.5: Statistics of differences (in mgals) between altimeter-derived gravity and two tracks of shipborne gravity anomalies in Taiwan Strait
Case Mean RMS Minimum Maximum
LSC with differenced height 7.91 9.82 -7.68 23.58
LSC with height slope 7.65 10.30 -9.13 28.30
LSC with DOV 9.39 12.16 -9.14 28.87
Inverse Vening Meinesz with DOV 9.14 11.61 -14.88 27.79
Table 5.6: Statistics of difference (in mgals) between altimeter-derived and shipborne gravity anomalies in the Taiwan Strait
Method and data for gravity derivation Mean RMS Min Max LSC with differenced heights only 8.01 9.06 -12.21 24.84
LSC with differenced heights and land gravity anomalies
6.22 8.22 -11.85 22.73
Figure 5.8: Gravity anomalies along Cruises c1217 and dmm07 in the East China Sea
Figure 5.9: Time series of normalized difference of gravity anomaly, standard error of ERS-1 SSH, tide model difference and depth, along Cruise dmm07.
Figure 5.10: Time series of normalized difference of gravity anomaly, standard error of ERS-1 SSH, tide model difference and depth, along Cruise c1217.
5.5.2 The Taiwan Strait
Next we carried out experiments over TS using the same four cases as in the ECS. We used shipborne gravity data along Tracks 1 and 2 (Figure 5.1) to evaluate the altimeter-derived gravity anomalies. These shipborne gravity data were compiled
by Hsu et al. (1998), who has crossover adjusted the shipborne gravity data and removed bad values. Table 5.5 shows the results of the comparisons between altimeter-derived and shipborne gravity anomalies in the four cases. The conclusion from Table 5.5 is similar to what has been drawn from Table 5.4, that is, the least square collocation method with DOV produces the worst result. Again, use of differenced heights produces the best results provided that the same altimeter-gravity conversion method is used.
Since land gravity data are available along the coast of TS, we also assessed the impact of land gravity data on the accuracy of altimeter-derived gravity anomaly.
Figure 5.11 shows the distribution of land gravity and altimeter data around Taiwan.
Note that there is no altimeter at the immediate coastal waters off the west coast of Taiwan. We experimented with the method of LSC using differenced heights, and with and without land gravity data (two cases). Table 5.6 shows the statistics of the differences between shipborne and altimeter-derived gravity anomalies. Figure 5.12 shows the shipborne and altimeter-derived gravity anomalies along Tracks 1 and 2.
The patterns of the difference along Tracks 1 and 2 are similar to those for Tracks c1217 and dmm07 (Figure 5.8). That is, the agreement between shipborne and altimeter-derived gravity anomalies at large spatial scales is better than that at small spatial scales. Furthermore, Tracks 1 and 2 are only tens of km off the west coast of Taiwan and the density of altimeter data is low along theses two tracks (Figure 5.11).
In general, difference of gravity anomaly increases with decreasing density of altimeter data. The density of land gravity data is relatively high over a zone from
5° .
22 N to 24.5°N, and here the agreement between altimeter-derived (with land gravity) and shipborne gravity anomalies is better than that in other parts of the ship tracks. In the areas south of 22.5°N and north of 24.5°N, only few land gravity data
are used, so there is virtually no difference between the altimeter-only gravity anomalies and the altimeter-land gravity anomalies.
Figure 5.11: Distribution of land gravity data and altimeter data around Taiwan.
Figure 5.12: Gravity anomalies along Track 1 and Track 2 in the Taiwan Strait.
Again, we investigated the possible causes of the difference between altimeter-derived and shipborne gravity anomalies in the TS. Figure 5.13 and 5.14 shows the same quantities as in Figure 5.9 and 5.10, but in the TS. Again, along the two ship tracks, the patterns of gravity anomaly difference are quite random and are
not correlated with depth and tidal height difference. However, there is a strong correlation (about 0.9) between standard error of ERS-1 SSH and tidal height difference along both Tracks 1 and 2. Again, tidal height difference increases as decreasing depth. The conclusions from the analyses associated with Figures 5.9 &
5.10 and Figures 5.13 & 5.14 are in agreement with the conclusion drawn in Section 5.2: the major source of large standard error of SSH and large error of altimeter-derived gravity anomaly is tide model error. Another cause of degraded altimeter-derived gravity anomaly near coasts, which is not investigated in this paper, is low altimeter data density due to data editing. Even the data editing criterion near coasts is relaxed to increase data density, the additional altimeter data may not be of good quality for gravity derivation. One way to improve altimeter data quality near coasts is to retrack waveforms of altimeter ranging. For example, Deng et al. (2003) have obtained improved T/P SSHs by waveform retracking over the Australian coasts.
Currently, globally retracked ERS-1 and Geosat waveforms are available (Lillibridge et al., 2004; Smith et al., 2004), and have been shown to produce improved marine gravity fields.
Figure 5.13: Time series of normalized difference of gravity anomaly, standard error of ERS-1 SSH, tide model difference and depth, along Track 1
Figure 5.14: Time series of normalized difference of gravity anomaly, standard error of ERS-1 SSH, tide model difference and depth, along Track 2.
CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
6.1 Conclusions
In this thesis, Chapter 2 first introduces 4 methods for gravity anomaly derivations from altimetry, which include a completely different kind of case, LSC with differenced height. Chapter 2 and 3 describe the work of an improved computation of global MSSH and gravity anomaly grids using improved multi-satellite altimeter data sets and a new procedure. Various tests have been made in order to find an optimal set of parameters for the computation. The procedure is based on the deflection-geoid and inverse Vening Meinesz formulas, as well as the remove-restore concept. The crossover adjustment of SSHs is not used because of the use of DOV as the altimeter data type in the computation. Using DOV is particularly advantageous over areas with sparse altimeter data and in the case of long wavelength error contained in altimeter data. The comparisons of the NCTU01 MSSH with the T/P and the ERS-1 MSSH result in overall RMS differences of 5.0 and 3.1 cm in SSH, respectively, and 7.1 and 3.2 µrad in SSH gradient, respectively.
The agreements between the predicted and shipborne gravity anomalies range from 3.0 to 13.4 mgals, depending on the gravity signatures and the altimeter data noise, the later being affected by instrument noise, sea state and accuracies of geophysical corrections. The NCTU01 MSSH model outperforms the NASA/GSFC model (Wang, 2001) and the CLS model, and the NCTU01 gravity anomaly model has a better accuracy than those of the models of Sandwell and Smith (1997) and Hwang et al.
(1998). The gravity anomalies described in Chapter 3 can be used to derive mean gravity anomalies for modeling high-degree geopotential coefficients, and to study the spectral properties of the Earth’s gravity field.
Chapter 4 compares two methods with three kinds of altimeter data types of gravity anomaly derivation from altimetry data. For the four computations of two methods, the RMS differences between altimetry-derived gravity anomalies and shipborne gravity anomalies are 9.06 (differenced height) and 9.59, 10.26 (height slope) and 9.77, 10.44 and 13.10, 10.73 and 11.86 mgals, over TS and ECS, respectively. Comparing to NCTU01 gravity anomaly model, the RMS differences are further reduced by 1.67 and 2.27 mgal in these two areas. The method of LSC with differenced heights yields promising results and produced the best accuracy over TS and ECS. An iterative method to remove outliers in along-track altimeter data improves altimeter data quality and improves the accuracy of predicted gravity anomaly. Preprocessing of altimeter data is important in obtaining good estimation of gravity. Good estimation of gravity depends on both good altimeter data and good method. Use of along-track DOV with LSC yields a better result over TS, but gives a worse result over ECS compared to the result from the inverse Vening Meinesz formula. However, the inverse Vening-Meinesz formula with 1D FFT is the fastest methods among the three methods.
Chapter 5 studies the sources of the differences among two global gravity anomaly grids over ECS and TS. We conclude that tide model error is the biggest contributor to the differences. It is found that tide model error, standard deviation of SSH and ocean depth are highly correlated. Also, the complicated sea states over these two areas increase the roughness of the sea surface and hence the noise level of altimeter ranging. As case studies, we experimented with the method of LSC using
differenced heights, and with and without land gravity data. Including land gravity data in the vicinity of coasts enhances the accuracy of altimeter-derived gravity anomalies. Future studies of gravity anomalies recovery will focus on shallow waters over the Yellow Sea, South China Sea and Southeast Asia.
6.2 Recommendations
For future work, we recommend a procedure to improve the accuracy of altimeter-derived gravity anomalies: (1) retrack near-shore waveforms of altimeter to produce waveform-corrected SSHs, (2) use the corrected SSHs to improve tide model, (3) use improved tide model to correct for the ocean tide effect in SSH. Finally, the improved tide-corrected and waveform-corrected altimeter data will lead to an improved gravity field over shallow waters. In addition, the altimeter derived gravity could be improved by merging the altimeter data available today with those derived from future and more accurate missions, and by combining with other sources of data, such as airborne observations and shipborne gravity data to do the prediction procedure.
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